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We present a general methodology for electromagnetic homogenization and characterization of bianisotropic metasurfaces formed by regular or random arrangements of small arbitrary inclusions at interfaces of two different isotropic media. The approach unites and generalizes the earlier theories developed independently by two joint research groups: that of profs. Holloway and Kuester and that of profs. Simovski and Tretyakov. We analyze the features of both formalisms and discuss their peculiarities in several example cases. Our theory can be used in the analysis and synthesis of a wide spectrum of metasurfaces. [ABSTRACT FROM AUTHOR]

Recently, it has been shown that a metasurface of plasmonic nanospheres deposited on a highly refractive substrate requires a bianisotropic magnetoelectric coupling for its effective description. The effect has been coined substrate-induced bianisotropy. It leads to an asymmetric reflectance similar to bianisotropic metasurfaces. In this work, through a circuit model, we show that such bianisotropy does not necessarily emerge for all substrated metasurfaces. Indeed, we show that the thickness of the metasurface plays a crucial role to encounter substrate-induced bianisotropy. Moreover, by taking advantage of substrate-induced bianisotropy, we present the necessary conditions for the circuit model parameters to compensate the asymmetric reflectance generated by an intrinsically bianisotropic metasurface. We finally express that, in substrated metasurfaces, the asymmetric reflectance and the bianisotropic response are two separate issues albeit with interdependencies. [ABSTRACT FROM AUTHOR]

We explore the optical properties of a meta-atom made of plasmonic nanopatches that possess an increasing degree of complexity. We show that if two nanopatches are strongly coupled and have a different geometrical footprint, the meta-atom exhibits a resonant magnetoelectric response, in addition to the anticipated resonant electric and magnetic response. Thus, it behaves similarly as the so-called omega particle, but with the unique advantage that frequency and strength of this magnetoelectric resonance can be independently tuned and modified with respect to the corresponding values of the electric resonance. This allows a metasurface of such meta-atoms to possess widely controlled reflection and transmission coefficients, e.g., the regimes of strongly asymmetric reflectance and perfect absorption become possible. Alternatively, an individual meta-atom of such kind can act as a directive nanoantenna with zero backscattered fields (Huygens' scatterer). [ABSTRACT FROM AUTHOR]

Understanding the impact of order and disorder is of fundamental importance to perceive and to appreciate the functionality of modern photonic metasurfaces. Metasurfaces with disordered and amorphous inner arrangements promise to mitigate problems that arise for their counterparts with strictly periodic lattices of elementary unit cells such as, e.g., spatial dispersion, and allows the use of fabrication techniques that are suitable for large scale and cheap fabrication of metasurfaces. In this study, we analytically, numerically and experimentally investigate metasurfaces with different lattice arrangements and uncover the influence of lattice disorder on their electromagnetic properties. The considered metasurfaces are composed of metal-dielectric-metal elements that sustain both electric and magnetic resonances. Emphasis is placed on understanding the effect of the transition of the lattice symmetry from a periodic to an amorphous state and on studying oblique illumination. For this scenario, we develop a powerful analytical model that yields, for the first time, an adequate description of the scattering properties of amorphous metasurfaces, paving the way for their integration into future applications. [ABSTRACT FROM AUTHOR]

We have revised the transmission line model with the purpose of simplifying the electromagnetic characterization of metasurfaces with both electric and magnetic responses. The revised model is an efficient tool for the case when a metasurface is located on top of a finite-thickness substrate or inside a finite-thickness slab. We have derived analytical expressions for the grid series impedance and shunt admittance of a substrated metasurface. The presented theory is illustrated by a numerical example of an array consisting of Mie-resonant silicon nanospheres. We have retrieved individual polarizabilities of a single sphere in a uniform host medium and compared them with the predictions of classical Mie theory. Further, we have studied a more practical case when the array of Si spheres is located on top of a finite-thickness glass substrate. [ABSTRACT FROM AUTHOR]

We discuss possible topologies of physically different metasurfaces with equivalent macroscopic electromagnetic responses. We specifically demonstrate that the presence of normal components (with respect to the metasurface plane) of the polarization currents does not add any functionality in engineering the reflection and transmission characteristics which cannot occur in metasurfaces maintaining only tangential currents. Therefore, if a certain property is achievable using general volumetric inclusions, polarizable along all three directions, the same response can be achieved using some equivalent perfectly planar elements, polarizable only in the metasurface plane. Our results clarify what physical properties are necessary for realizing desired metasurface responses and promote flat microwave and optical designs, providing possibilities for dramatic complexity reduction of metasurfaces for rather general field transformations, including asymmetric reflection and transmission. [ABSTRACT FROM AUTHOR]

The polarization response of molecules or meta-atoms to external electric and magnetic fields, which defines the electromagnetic properties of materials, can either be direct (electric field induces electric moment and magnetic field induces magnetic moment) or indirect (magnetoelectric coupling in bianisotropic scatterers). Earlier studies suggest that there is a fundamental bound on the indirect response of all passive scatterers: It is believed to be always weaker than the direct one. In this paper, we prove that there exist scatterers which overcome this bound substantially. Moreover, we show that the amplitudes of electric and magnetic polarizabilities can be negligibly small as compared to the magnetoelectric coupling coefficients. However, we prove that if at least one of the direct-excitation coefficients vanishes, magnetoelectric coupling effects in passive scatterers cannot exist. Our findings open a way to a new class of electromagnetic scatterers and composite materials. [ABSTRACT FROM AUTHOR]

Nonuniform metasurfaces (electrically thin composite layers) can be used for shaping refracted and reflected electromagnetic waves. However, known design approaches based on the generalized refraction and reflection laws do not allow realization of perfectly performing devices: there are always some parasitic reflections into undesired directions. In this paper we introduce and discuss a general approach to the synthesis of metasurfaces for full control of transmitted and reflected plane waves and show that perfect performance can be realized. The method is based on the use of an equivalent impedance matrix model which connects the tangential field components at the two sides on the metasurface. With this approach we are able to understand what physical properties of the metasurface are needed in order to perfectly realize the desired response. Furthermore, we determine the required polarizabilities of the metasurface unit cells and discuss suitable cell structures. It appears that only spatially dispersive metasurfaces allow realization of perfect refraction and reflection of incident plane waves into arbitrary directions. In particular, ideal refraction is possible only if the metasurface is bianisotropic (weak spatial dispersion), and ideal reflection without polarization transformation requires spatial dispersion with a specific, strongly nonlocal response to the fields. [ABSTRACT FROM AUTHOR]

In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of regular and random grids and explain recently observed dramatic differences in resonance broadening in the electric and magnetic modes of random arrays. We show that randomness in the particle positioning influences equally on the scattering loss from both electric and magnetic dipoles, however, the observed resonance broadening can be very different depending on the absorption level in different modes as well as on the average electrical distance between the particles. The theory is illustrated by an example of a planar metasurface composed of cut-wire pairs. We show that in this particular case at the magnetic resonance the array response is almost not affected by positioning randomness due to lower frequency and higher absorption losses in that mode. The developed model allows predictions of behavior of random grids based on the knowledge of polarizabilities of single inclusions. [ABSTRACT FROM AUTHOR]

Genuinely homogeneous metamaterials, which may be characterized by local effective constitutive relations, are required for many spectacular metamaterial applications. Such metamaterials have to be made of meta-atoms, i.e., subwavelength resonators, which exhibit only electric and or magnetic dipole and negligible higher-order multipolar polarizabilities in the spectral range of interest. Here, we show that these desired meta-atoms can be designed by exploiting the extreme coupling regime. Appropriate meta-atoms are identified by performing a multipole analysis of the field scattered from the respective meta-atom. To design those particular meta-atoms it is important to disclose the frequency and angular-dependent polarizability of both dipole moments. We demonstrate the applicability of a purely analytical model to accurately calculate for a normally incident plane wave reflection and transmission from meta-surfaces made of periodically arranged meta-atoms. With our work we identify a possible route towards the engineering of artificial materials while only considering the response from its constituents. Our approach is generally applicable to all spectral domains and can be used to evaluate and design metamaterials made from different constituting materials, e.g., metals, dielectrics, or semiconductors. [ABSTRACT FROM AUTHOR]